E. B. Davies, Dynamical stability of metastable states, Journal of Functional Analysis, vol.46, issue.3, pp.373-386, 1982.
DOI : 10.1016/0022-1236(82)90052-0

E. B. Davies, Metastable States of Symmetric Markov Semigroups I, Proc. London Math. Soc, pp.133-150, 1982.
DOI : 10.1112/plms/s3-45.1.133

E. B. Davies, Metastable States of Symmetric Markov Semigroups II, Journal of the London Mathematical Society, vol.2, issue.3, pp.541-556, 1982.
DOI : 10.1112/jlms/s2-26.3.541

M. V. Day, On the exponential exit law in the small parameter exit problem, Stochastics, vol.17, issue.4, pp.297-323, 1983.
DOI : 10.1070/RM1970v025n01ABEH001254

M. V. Day, Mathematical Approaches to the Problem of Noise-Induced Exit, Stochastic Analysis, Control, Optimization and Applications, pp.269-287, 1999.
DOI : 10.1007/978-1-4612-1784-8_16

C. Dellago, P. G. Bolhuis, and P. L. Geissler, Transition Path Sampling Methods, Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology, pp.349-391, 2006.
DOI : 10.1007/3-540-35273-2_10

G. , D. Gesù, T. Lelì-evre, D. L. Peutrec, and B. Nectoux, The exit from a metastable state: concentration of the exit point on the low energy saddle points, 2017.

G. , D. Gesù, T. Lelì-evre, D. L. Peutrec, and B. Nectoux, Jump markov models and transition state theory: the quasi-stationary distribution approach, Faraday Discussions, vol.195, pp.469-495, 2017.

G. , D. Gesù, T. Lelì-evre, D. L. Peutrec, and B. Nectoux, Sharp asymptotics of the first exit point density, 2017.

M. Eckhoff, Precise asymptotics of small eigenvalues of reversible diffusions in the metastable regime, The Annals of Probability, vol.33, issue.1, pp.244-299, 2005.
DOI : 10.1214/009117904000000991

L. C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol.19, 2010.

Y. Fan, S. Yip, and B. Yildiz, Autonomous basin climbing method with sampling of multiple transition pathways: application to anisotropic diffusion of point defects in hcp Zr, Journal of Physics: Condensed Matter, vol.26, issue.36, p.365402, 2014.
DOI : 10.1088/0953-8984/26/36/365402

M. I. Freidlin and A. D. , Random Perturbations of Dynamical Systems, 1984.

A. Galves, E. Olivieri, and M. E. Vares, Metastability for a class of dynamical systems subject to small random perturbations. The Annals of Probability, pp.1288-1305, 1987.

V. Gol-'dshtein, I. Mitrea, and M. Mitrea, Hodge decompositions with mixed boundary conditions and applications to partial differential equations on lipschitz manifolds, Journal of Mathematical Sciences, vol.57, issue.5, pp.347-400, 2011.
DOI : 10.1512/iumj.2008.57.3338

P. Hänggi, P. Talkner, and M. Borkovec, Reaction-rate theory: fifty years after Kramers, Reviews of Modern Physics, vol.35, issue.2, pp.251-342, 1990.
DOI : 10.1103/PhysRevB.35.4737

B. Helffer, Introduction to the semiclassical analysis for the Schrödinger operator and applications, 1988.

B. Helffer, Semi-classical analysis for the Schrödinger operator and applications, 2006.

B. Helffer, M. Klein, and F. Nier, Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary, Mémoires de la Société mathématique de France, vol.1, pp.41-85, 2004.
DOI : 10.24033/msmf.417

URL : https://hal.archives-ouvertes.fr/hal-00002744

B. Helffer and F. Nier, Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary, Mémoires de la Société mathématique de France, vol.1, 2006.
DOI : 10.24033/msmf.417

URL : https://hal.archives-ouvertes.fr/hal-00002744

B. Helffer and J. Sjöstrand, Multiple wells in the semi-classical limit I, Communications in Partial Differential Equations, vol.52, issue.2, pp.337-408, 1984.
DOI : 10.1016/0022-1236(83)90085-X

B. Helffer and J. Sjöstrand, Multiple Wells in the Semi-Classical Limit III - Interaction Through Non-Resonant Wells, Mathematische Nachrichten, vol.14, issue.1, pp.263-313, 1985.
DOI : 10.1007/BF02791064

B. Helffer and J. Sjöstrand, Puits multiples en limite semi-classique. II. interaction moléculaire. symétries. perturbation, pp.127-212, 1985.

B. Helffer and J. Sjöstrand, Puits multiples en limite semi-classique V-Etude des minipuits. Current topics in partial differential equations, pp.133-186, 1986.
DOI : 10.1080/03605308508820379

B. Helffer and J. Sjöstrand, R??sonances en limite semi-classique, Mémoires de la Société mathématique de France, vol.1, pp.1-228, 1986.
DOI : 10.24033/msmf.327

F. Hérau, M. Hitrik, and J. Sjöstrand, Tunnel effect and symmetries for Kramers???Fokker???Planck type operators, Journal of the Institute of Mathematics of Jussieu, vol.40, issue.15, pp.567-634, 2011.
DOI : 10.4171/JEMS/14

R. A. Holley, S. Kusuoka, and D. W. Stroock, Asymptotics of the spectral gap with applications to the theory of simulated annealing, Journal of Functional Analysis, vol.83, issue.2, pp.333-347, 1989.
DOI : 10.1016/0022-1236(89)90023-2

T. Jakab, I. Mitrea, and M. Mitrea, On the regularity of differential forms satisfying mixed boundary conditions in a class of Lipschitz domains, Indiana University Mathematics Journal, vol.58, issue.5, pp.2043-2071, 2009.
DOI : 10.1512/iumj.2009.58.3678

S. Kamin, On Elliptic Singular Perturbation Problems with Turning Points, SIAM Journal on Mathematical Analysis, vol.10, issue.3, pp.447-455, 1979.
DOI : 10.1137/0510041

S. Karlin, E. Howard, and . Taylor, A second course in stochastic processes, 1981.

C. Kipnis and C. M. Newman, The Metastable Behavior of Infrequently Observed, Weakly Random, One-Dimensional Diffusion Processes, SIAM Journal on Applied Mathematics, vol.45, issue.6, pp.972-982, 1985.
DOI : 10.1137/0145059

C. , L. Bris, T. Lelì-evre, M. Luskin, and D. Perez, A mathematical formalization of the parallel replica dynamics, pp.119-146, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00596161

D. and L. Peutrec, Small eigenvalues of the Neumann realization of the semiclassical Witten Laplacian, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.19, issue.3-4, pp.3-4735, 2010.
DOI : 10.5802/afst.1265

URL : https://hal.archives-ouvertes.fr/hal-00297207

T. Lelì-evre, M. Rousset, and G. Stoltz, Free energy computations: A mathematical perspective, World Scientific, 2010.

R. S. Maier and D. L. Stein, Escape problem for irreversible systems, Physical Review E, vol.53, issue.2, pp.931-938, 1993.
DOI : 10.1007/978-1-4612-6380-7

URL : http://arxiv.org/pdf/chao-dyn/9303017v2.pdf

R. S. Maier and D. L. Stein, Limiting Exit Location Distributions in the Stochastic Exit Problem, SIAM Journal on Applied Mathematics, vol.57, issue.3, pp.752-790, 1997.
DOI : 10.1137/S0036139994271753

R. Marcelin, ContributionàContributionà l'´ etude de la cinétique physico-chimique, Ann. Physique, vol.3, pp.120-231, 1915.
DOI : 10.1051/anphys/191509030120

P. Mathieu, Zero white noise limit through Dirichlet forms, with application to diffusions in a random medium. Probability Theory and Related Fields, pp.549-580, 1994.

P. Mathieu, Spectra, exit times and long time asymptotics in the zero-whitenoise limit, Stochastics: An International Journal of Probability and Stochastic Processes, vol.55, issue.12, pp.1-20, 1995.

]. L. Michel, About small eigenvalues of Witten laplacian. arXiv preprint, 2017.

L. Miclo, Comportement de spectres d'opérateurs de SchrödingerSchrödingerà basse température, Bulletin des sciences mathématiques, vol.119, issue.6, pp.529-554, 1995.

T. Naeh, M. M. Klosek, B. J. Matkowsky, and Z. Schuss, A Direct Approach to the Exit Problem, SIAM Journal on Applied Mathematics, vol.50, issue.2, pp.595-627, 1990.
DOI : 10.1137/0150036

B. Perthame, Perturbed dynamical systems with an attracting singularity and weak viscosity limits in Hamilton-Jacobi equations. Transactions of the, pp.723-748, 1990.

M. Schilder, Some asymptotic formulas for Wiener integrals. Transactions of the, pp.63-85, 1966.

Z. Schuss, Theory and applications of stochastic processes: an analytical approach, 2009.
DOI : 10.1007/978-1-4419-1605-1

Z. Schuss and B. J. Matkowsky, The Exit Problem: A New Approach to Diffusion Across Potential Barriers, SIAM Journal on Applied Mathematics, vol.36, issue.3, pp.604-623, 1979.
DOI : 10.1137/0136043

C. Schütte, Conformational dynamics: modelling, theory, algorithm and application to biomolecules, 1998.

C. Schütte and M. Sarich, Metastability and Markov state models in molecular dynamics, Courant Lecture Notes, vol.24, 2013.
DOI : 10.1090/cln/024

M. R. Sorensen and A. F. Voter, Temperature-accelerated dynamics for simulation of infrequent events, The Journal of Chemical Physics, vol.91, issue.21, pp.9599-9606, 2000.
DOI : 10.1103/PhysRevLett.76.4927

M. Sugiura, Metastable behaviors of diffusion processes with small parameter, Journal of the Mathematical Society of Japan, vol.47, issue.4, pp.755-788, 1995.
DOI : 10.2969/jmsj/04740755

T. Swinburne, Stochastic Dynamics of Crystal Defects, 2015.
DOI : 10.1007/978-3-319-20019-4

E. Vanden-eijnden, Transition path theory, Computer Simulations in Condensed Matter Systems: From Materials to Chemical Biology, vol.1, pp.453-493, 2006.
DOI : 10.1007/3-540-35273-2_13

G. H. Vineyard, Frequency factors and isotope effects in solid state rate processes, Journal of Physics and Chemistry of Solids, vol.3, issue.1-2, pp.121-127, 1957.
DOI : 10.1016/0022-3697(57)90059-8

A. F. Voter, Parallel replica method for dynamics of infrequent events, Physical Review B, vol.29, issue.22, pp.13-985, 1998.
DOI : 10.1103/PhysRevB.29.6443

A. F. Voter, Radiation Effects in Solids, chapter Introduction to the Kinetic Monte Carlo Method, 2005.

D. J. Wales, Energy landscapes, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01423280

A. M. Yaglom, Certain limit theorems of the theory of branching random processes, Doklady Akad. Nauk SSSR (NS), p.3, 1947.

]. L. Bibliography-of-chapter, N. Ambrosio, D. Fusco, and . Pallara, Functions of bounded variation and free discontinuity problems, 2000.

N. Berglund, Kramers' law: Validity, derivations and generalisations, Markov Processes Relat. Fields, vol.19, pp.459-490, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00604399

A. Binder, T. Lelì, and G. Simpson, A generalized parallel replica dynamics, Journal of Computational Physics, vol.284, pp.595-616, 2015.
DOI : 10.1016/j.jcp.2015.01.002

F. Bouchet and J. Reygner, Generalisation of the Eyring???Kramers Transition Rate Formula to Irreversible Diffusion Processes, Annales Henri Poincar??, vol.36, issue.3, pp.3499-3532, 2016.
DOI : 10.1137/0136043

URL : https://hal.archives-ouvertes.fr/ensl-01174112

A. Bovier, M. Eckhoff, V. Gayrard, and M. Klein, Metastability in Reversible Diffusion Processes I: Sharp Asymptotics for Capacities and Exit Times, Journal of the European Mathematical Society, vol.6, pp.399-424, 2004.
DOI : 10.4171/JEMS/14

A. Bovier, V. Gayrard, and M. Klein, Metastability in reversible diffusion processes II: precise asymptotics for small eigenvalues, Journal of the European Mathematical Society, vol.7, pp.69-99, 2005.
DOI : 10.4171/JEMS/22

G. R. Bowman, V. S. Pande, and F. Noé, An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation, 2014.
DOI : 10.1007/978-94-007-7606-7

R. Brown, The mixed problem for laplace's equation in a class of lipschitz domains, Communications in Partial Differential Equations, vol.8, issue.7-8, pp.1217-1233, 1994.
DOI : 10.1016/0022-1236(84)90066-1

M. Cameron, Computing the asymptotic spectrum for networks representing energy landscapes using the minimum spanning tree, Networks and Heterogeneous Media, vol.9, issue.3, pp.383-416, 2014.
DOI : 10.3934/nhm.2014.9.383

K. C. Chang and J. Liu, A cohomology complex for manifolds with boundary. Topological methods in non linear analysis, pp.325-340, 1995.

P. Collet, S. Martínez, and J. San-martín, Quasi-Stationary Distributions, 2013.
DOI : 10.1007/978-3-642-33131-2

URL : https://hal.archives-ouvertes.fr/hal-00431844

H. L. Cycon, R. G. Froese, W. Kirsch, and B. Simon, Schrödinger operators with application to quantum mechanics and global geometry, 1987.

M. V. Day, On the exponential exit law in the small parameter exit problem, Stochastics, vol.17, issue.4, pp.297-323, 1983.
DOI : 10.1070/RM1970v025n01ABEH001254

M. V. Day, Mathematical Approaches to the Problem of Noise-Induced Exit, Stochastic Analysis, Control, Optimization and Applications, pp.269-287, 1999.
DOI : 10.1007/978-1-4612-1784-8_16

G. , D. Gesù, T. Lelì-evre, D. L. Peutrec, and B. Nectoux, The exit from a metastable state: concentration of the exit point on the low energy saddle points, 2017.

G. , D. Gesù, T. Lelì-evre, D. L. Peutrec, and B. Nectoux, Jump markov models and transition state theory: the quasi-stationary distribution approach, Faraday Discussions, vol.195, pp.469-495, 2017.

M. Dimassi and J. Sjöstrand, Spectral asymptotics in the semi-classical limit. Number 268, 1999.

M. Eckhoff, Precise asymptotics of small eigenvalues of reversible diffusions in the metastable regime, The Annals of Probability, vol.33, issue.1, pp.244-299, 2005.
DOI : 10.1214/009117904000000991

A. Eizenberg, The exponential leveling and the Ventcel-Freidlin ???minimal action??? function, Journal d'Analyse Math??matique, vol.25, issue.1, pp.99-111, 1990.
DOI : 10.1080/17442508408833304

L. C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol.19, 2010.

L. C. Evans and R. F. Gariepy, Measure theory and fine properties of functions, Studies in Advanced Mathematics, 1992.

Y. Fan, S. Yip, and B. Yildiz, Autonomous basin climbing method with sampling of multiple transition pathways: application to anisotropic diffusion of point defects in hcp Zr, Journal of Physics: Condensed Matter, vol.26, issue.36, p.365402, 2014.
DOI : 10.1088/0953-8984/26/36/365402

M. I. Freidlin and A. D. , Random Perturbations of Dynamical Systems, 1984.

A. Galves, E. Olivieri, and M. E. Vares, Metastability for a class of dynamical systems subject to small random perturbations. The Annals of Probability, pp.1288-1305, 1987.

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, 2001.

V. Gol-'dshtein, I. Mitrea, and M. Mitrea, Hodge decompositions with mixed boundary conditions and applications to partial differential equations on lipschitz manifolds, Journal of Mathematical Sciences, vol.57, issue.5, pp.347-400, 2011.
DOI : 10.1512/iumj.2008.57.3338

P. Hänggi, P. Talkner, and M. Borkovec, Reaction-rate theory: fifty years after Kramers, Reviews of Modern Physics, vol.35, issue.2, pp.251-342, 1990.
DOI : 10.1103/PhysRevB.35.4737

B. Helffer, Introduction to the semiclassical analysis for the Schrödinger operator and applications, 1988.

B. Helffer, Semi-classical analysis for the Schrödinger operator and applications, 2006.

B. Helffer, Spectral theory and its applications, 2013.
DOI : 10.1017/CBO9781139505727

B. Helffer, M. Klein, and F. Nier, Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary, Mémoires de la Société mathématique de France, vol.1, pp.41-85, 2004.
DOI : 10.24033/msmf.417

URL : https://hal.archives-ouvertes.fr/hal-00002744

B. Helffer and F. Nier, Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary, Mémoires de la Société mathématique de France, vol.1, 2006.
DOI : 10.24033/msmf.417

URL : https://hal.archives-ouvertes.fr/hal-00002744

B. Helffer and J. Sjöstrand, Multiple wells in the semi-classical limit I, Communications in Partial Differential Equations, vol.52, issue.2, pp.337-408, 1984.
DOI : 10.1016/0022-1236(83)90085-X

B. Helffer and J. Sjöstrand, Multiple Wells in the Semi-Classical Limit III - Interaction Through Non-Resonant Wells, Mathematische Nachrichten, vol.14, issue.1, pp.263-313, 1985.
DOI : 10.1007/BF02791064

B. Helffer and J. Sjöstrand, Puits multiples en limite semi-classique. II. Interaction moléculaire. Symétries. Perturbation. Annales de l'IHP Physique théorique, pp.127-212, 1985.

B. Helffer and J. Sjöstrand, Puits multiples en mecanique semi-classique iv etude du complexe de witten, Communications in Partial Differential Equations, vol.17, issue.4, pp.245-340, 1985.
DOI : 10.1515/9781400878055

B. Helffer and J. Sjöstrand, R??sonances en limite semi-classique, Mémoires de la Société mathématique de France, vol.1, pp.1-228, 1986.
DOI : 10.24033/msmf.327

R. A. Holley, S. Kusuoka, and D. W. Stroock, Asymptotics of the spectral gap with applications to the theory of simulated annealing, Journal of Functional Analysis, vol.83, issue.2, pp.333-347, 1989.
DOI : 10.1016/0022-1236(89)90023-2

T. Jakab, I. Mitrea, and M. Mitrea, On the regularity of differential forms satisfying mixed boundary conditions in a class of Lipschitz domains, Indiana University Mathematics Journal, vol.58, issue.5, pp.2043-2071, 2009.
DOI : 10.1512/iumj.2009.58.3678

C. Kipnis and C. M. Newman, The Metastable Behavior of Infrequently Observed, Weakly Random, One-Dimensional Diffusion Processes, SIAM Journal on Applied Mathematics, vol.45, issue.6, pp.972-982, 1985.
DOI : 10.1137/0145059

H. A. Kramers, Brownian motion in a field of force and the diffusion model of chemical reactions, Physica, vol.7, issue.4, pp.284-304, 1940.
DOI : 10.1016/S0031-8914(40)90098-2

F. Laudenbach, A Morse complex on manifolds with boundary, Geometriae Dedicata, vol.17, issue.4, pp.47-57, 2011.
DOI : 10.2307/1970311

URL : https://hal.archives-ouvertes.fr/hal-00466294

C. , L. Bris, T. Lelì-evre, M. Luskin, and D. Perez, A mathematical formalization of the parallel replica dynamics, pp.119-146, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00596161

D. and L. Peutrec, Small eigenvalues of the Neumann realization of the semiclassical Witten Laplacian, Annales de la facult?? des sciences de Toulouse Math??matiques, vol.19, issue.3-4, pp.3-4735, 2010.
DOI : 10.5802/afst.1265

URL : https://hal.archives-ouvertes.fr/hal-00297207

T. Lelì-evre and F. Nier, Low temperature asymptotics for quasistationary distributions in a bounded domain, Analysis & PDE, vol.17, issue.3, pp.561-628, 2015.
DOI : 10.1142/9789812386588

P. Lions, Generalized solutions of Hamilton-Jacobi equations, 1982.

R. S. Maier and D. L. Stein, Escape problem for irreversible systems, Physical Review E, vol.53, issue.2, pp.931-938, 1993.
DOI : 10.1007/978-1-4612-6380-7

R. S. Maier and D. L. Stein, Limiting Exit Location Distributions in the Stochastic Exit Problem, SIAM Journal on Applied Mathematics, vol.57, issue.3, pp.752-790, 1997.
DOI : 10.1137/S0036139994271753

R. Marcelin, ContributionàContributionà l'´ etude de la cinétique physico-chimique, Ann. Physique, vol.3, pp.120-231, 1915.
DOI : 10.1051/anphys/191509030120

P. Mathieu, Zero white noise limit through Dirichlet forms, with application to diffusions in a random medium. Probability Theory and Related Fields, pp.549-580, 1994.

P. Mathieu, Spectra, exit times and long time asymptotics in the zero-whitenoise limit, Stochastics: An International Journal of Probability and Stochastic Processes, vol.55, issue.12, pp.1-20, 1995.

B. J. Matkowsky and Z. Schuss, The Exit Problem for Randomly Perturbed Dynamical Systems, SIAM Journal on Applied Mathematics, vol.33, issue.2, pp.365-382, 1977.
DOI : 10.1137/0133024

]. L. Miclo, Comportement de spectres d'opérateurs de schrödinger a basse température, Bulletin des sciences mathématiques, vol.119, issue.6, pp.529-554, 1995.

T. Naeh, M. M. Klosek, B. J. Matkowsky, and Z. Schuss, A Direct Approach to the Exit Problem, SIAM Journal on Applied Mathematics, vol.50, issue.2, pp.595-627, 1990.
DOI : 10.1137/0150036

]. F. Nier, Boundary Conditions and Subelliptic Estimates for Geometric Kramers-Fokker-Planck Operators on Manifolds with Boundaries, Memoirs of the American Mathematical Society, vol.252, issue.1200, 2014.
DOI : 10.1090/memo/1200

URL : https://hal.archives-ouvertes.fr/hal-00863866

B. Perthame, Perturbed dynamical systems with an attracting singularity and weak viscosity limits in Hamilton-Jacobi equations. Transactions of the, pp.723-748, 1990.

C. Pugh, Real mathematical analysis, 2002.
DOI : 10.1007/978-0-387-21684-3

Z. Schuss, Theory and applications of stochastic processes: an analytical approach, 2009.
DOI : 10.1007/978-1-4419-1605-1

Z. Schuss and B. J. Matkowsky, The Exit Problem: A New Approach to Diffusion Across Potential Barriers, SIAM Journal on Applied Mathematics, vol.36, issue.3, pp.604-623, 1979.
DOI : 10.1137/0136043

C. Schütte, Conformational dynamics: modelling, theory, algorithm and application to biomolecules, 1998.

C. Schütte and M. Sarich, Metastability and Markov state models in molecular dynamics, Courant Lecture Notes, vol.24, 2013.
DOI : 10.1090/cln/024

G. Schwarz, Hodge decomposition?a method for solving boundary value problems, Lecture Notes in Mathematics, vol.1607, 1995.
DOI : 10.1007/BFb0095978

B. Simon, Semiclassical Analysis of Low Lying Eigenvalues, II. Tunneling, The Annals of Mathematics, vol.120, issue.1, pp.89-118, 1984.
DOI : 10.2307/2007072

M. R. Sorensen and A. F. Voter, Temperature-accelerated dynamics for simulation of infrequent events, The Journal of Chemical Physics, vol.91, issue.21, pp.9599-9606, 2000.
DOI : 10.1103/PhysRevLett.76.4927

M. Sugiura, Metastable behaviors of diffusion processes with small parameter, Journal of the Mathematical Society of Japan, vol.47, issue.4, pp.755-788, 1995.
DOI : 10.2969/jmsj/04740755

G. H. Vineyard, Frequency factors and isotope effects in solid state rate processes, Journal of Physics and Chemistry of Solids, vol.3, issue.1-2, pp.121-127, 1957.
DOI : 10.1016/0022-3697(57)90059-8

A. F. Voter, A method for accelerating the molecular dynamics simulation of infrequent events, The Journal of Chemical Physics, vol.91, issue.11, pp.4665-4677, 1997.
DOI : 10.1063/1.465284

A. F. Voter, Parallel replica method for dynamics of infrequent events, Physical Review B, vol.29, issue.22, pp.13-985, 1998.
DOI : 10.1103/PhysRevB.29.6443

A. F. Voter, Radiation Effects in Solids, chapter Introduction to the Kinetic Monte Carlo Method, 2005.

D. J. Wales, Energy landscapes, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01423280

E. Witten, Supersymmetry and Morse theory, Journal of Differential Geometry, vol.17, issue.4, pp.661-692, 1982.
DOI : 10.4310/jdg/1214437492

URL : https://doi.org/10.4310/jdg/1214437492

A. Bovier, M. Eckhoff, V. Gayrard, and M. Klein, Metastability in Reversible Diffusion Processes I: Sharp Asymptotics for Capacities and Exit Times, Journal of the European Mathematical Society, vol.6, issue.4, pp.399-424, 2004.
DOI : 10.4171/JEMS/14

A. Bovier, V. Gayrard, and M. Klein, Metastability in reversible diffusion processes II: precise asymptotics for small eigenvalues, Journal of the European Mathematical Society, vol.7, issue.1, pp.69-99, 2005.
DOI : 10.4171/JEMS/22

M. Cameron, Computing the asymptotic spectrum for networks representing energy landscapes using the minimum spanning tree, Networks and Heterogeneous Media, vol.9, issue.3, pp.383-416, 2014.
DOI : 10.3934/nhm.2014.9.383

M. Day, Exponential Leveling for Stochastically Perturbed Dynamical Systems, SIAM Journal on Mathematical Analysis, vol.13, issue.4, pp.532-540, 1982.
DOI : 10.1137/0513035

M. Day, Mathematical Approaches to the Problem of Noise-Induced Exit, Stochastic Analysis, Control, Optimization and Applications, pp.269-287, 1999.
DOI : 10.1007/978-1-4612-1784-8_16

G. , D. Gesù, D. Le-peutrec, T. Lelì, and B. Nectoux, Sharp asymptotics of the first exit point density, 2017.

A. Eizenberg, The exponential leveling in elliptic singular perturbation problems with complicated attractors, Journal d'Analyse Math??matique, vol.31, issue.6, pp.229-249, 1990.
DOI : 10.1007/978-1-4684-0176-9

L. C. Evans, Partial differential equations, Graduate Studies in Mathematics, vol.19, 2010.

Y. Fan, S. Yip, and B. Yildiz, Autonomous basin climbing method with sampling of multiple transition pathways: application to anisotropic diffusion of point defects in hcp Zr, Journal of Physics: Condensed Matter, vol.26, issue.36, p.365402, 2014.
DOI : 10.1088/0953-8984/26/36/365402

M. I. Freidlin and A. D. , Random Perturbations of Dynamical Systems, 1984.

D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, 2001.

P. Hänggi, P. Talkner, and M. Borkovec, Reaction-rate theory: fifty years after Kramers, Reviews of Modern Physics, vol.35, issue.2, pp.251-342, 1990.
DOI : 10.1103/PhysRevB.35.4737

B. Helffer, M. Klein, and F. Nier, Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary, Mémoires de la Société mathématique de France, vol.1, pp.41-85, 2004.
DOI : 10.24033/msmf.417

URL : https://hal.archives-ouvertes.fr/hal-00002744

B. Helffer and F. Nier, Quantitative analysis of metastability in reversible diffusion processes via a Witten complex approach: the case with boundary, Mémoires de la Société mathématique de France, vol.1, issue.105, p.89, 2006.
DOI : 10.24033/msmf.417

URL : https://hal.archives-ouvertes.fr/hal-00002744

B. Helffer and J. Sjöstrand, Puits multiples en mecanique semi-classique iv etude du complexe de witten, Communications in partial differential equations, pp.245-340, 1985.
DOI : 10.1515/9781400878055

F. Hérau, M. Hitrik, and J. Sjöstrand, Tunnel effect and symmetries for Kramers???Fokker???Planck type operators, Journal of the Institute of Mathematics of Jussieu, vol.40, issue.15, pp.567-634, 2011.
DOI : 10.4171/JEMS/14

S. Kamin, On Elliptic Singular Perturbation Problems with Turning Points, SIAM Journal on Mathematical Analysis, vol.10, issue.3, pp.447-455, 1979.
DOI : 10.1137/0510041

C. , L. Bris, T. Lelì-evre, M. Luskin, and D. Perez, A mathematical formalization of the parallel replica dynamics, pp.119-146, 2012.
URL : https://hal.archives-ouvertes.fr/hal-00596161

D. and L. Peutrec, Small singular values of an extracted matrix of a Witten complex, Cubo, A Mathematical Journal, vol.11, issue.4, pp.49-57, 2009.

T. Lelì-evre and F. Nier, Low temperature asymptotics for quasistationary distributions in a bounded domain, Analysis & PDE, vol.17, issue.3, pp.561-628, 2015.
DOI : 10.1142/9789812386588

B. J. Matkowsky and Z. Schuss, The Exit Problem for Randomly Perturbed Dynamical Systems, SIAM Journal on Applied Mathematics, vol.33, issue.2, pp.365-382, 1977.
DOI : 10.1137/0133024

J. Milnor, Morse Theory.(AM-51, 2016.
DOI : 10.1515/9781400881802

L. Nirenberg, On Elliptic Partial Differential Equations, Il principio di minimo e sue applicazioni alle equazioni funzionali, pp.1-48, 2011.
DOI : 10.1007/978-3-642-10926-3_1

B. Perthame, Perturbed dynamical systems with an attracting singularity and weak viscosity limits in Hamilton-Jacobi equations. Transactions of the, pp.723-748, 1990.

C. Schütte, Conformational dynamics: modelling, theory, algorithm and application to biomolecules, 1998.

C. Schütte and M. Sarich, Metastability and Markov state models in molecular dynamics, Courant Lecture Notes, vol.24, 2013.
DOI : 10.1090/cln/024

G. Schwarz, Hodge decomposition?a method for solving boundary value problems, Lecture Notes in Mathematics, vol.1607, 1995.
DOI : 10.1007/BFb0095978

B. Simon, Trace ideals and their applications, 1979.
DOI : 10.1090/surv/120

A. F. Voter, Radiation Effects in Solids, chapter Introduction to the Kinetic Monte Carlo Method, 2005.

D. J. Wales, Energy landscapes, 2003.
URL : https://hal.archives-ouvertes.fr/hal-01423280

E. Witten, Supersymmetry and Morse theory, Journal of Differential Geometry, vol.17, issue.4, pp.661-692, 1982.
DOI : 10.4310/jdg/1214437492

URL : https://doi.org/10.4310/jdg/1214437492